A machine learning solutions approach of a time-delayed stochastic $ \tilde{S}\tilde{E}\tilde{I}\tilde{R}\tilde{V} $ model

In this work, we analyze the dynamics of a stochastic $ \tilde{S}\tilde{E}\tilde{I}\tilde{R}\tilde{V} $ model with a time delay. We mainly investigate the time delay's influence on these classes' asymptotic behavior. Furthermore, we examine the existence and stability of disease-free and endemic equilibrium points. To better understand the parameter's effects on the spread of an epidemic, we integrate artificial neural networks with the Bayesian regularization method. Additionally, leveraging physics-informed artificial intelligence (AI) and specialized machine training, we develop an advanced framework for solving systems of partial differential equations (PDEs). This approach enhances the accuracy of predictions and facilitates the optimal control and effective implementation of real-world epidemic management strategies.